A decorated tree approach to random permutations in substitution-closed classes

Abstract

International audienceWe establish a novel bijective encoding that represents permutations as forests ofdecorated (or enriched) trees. This allows us to prove local convergence of uniformrandom permutations from substitution-closed classes satisfying a criticality constraint.It also enables us to reprove and strengthen permuton limits for these classes in anew way, that uses a semi-local version of Aldous’ skeleton decomposition for size-constrained Galton–Watson trees